If I have a square matrix of arrays such as:
[1,2], [2,3]
[5,9], [1,4]
And I want to get the mean of the first values in the arrays of each row such:
1.5
3
Is this possible in Matlab?
I've used the mean(matrix, 2) command to do this with a matrix of single values, but I'm not sure how to extend this to deal with the arrays.
Get the first elements in all arrays of matrix, then call mean function
mean(matrix(:,:,1))
maybe you need to reshape before call mean
a = matrix(:,:,1);
mean(a(:))
You can apply mean function inside mean function to get the total mean value of the 2D array at index 1. You can do similary with array at index 2. Consider the following snapshot.
After staring at your problem for a long time, it looks like your input is a 3D matrix where each row of your formatting corresponds to a 2D matrix slice. Therefore, in proper MATLAB syntax, your matrix is actually:
M = cat(3, [1,2; 2,3], [5,9; 1,4]);
We thus get:
>> M = cat(3, [1,2; 2,3], [5,9; 1,4])
M(:,:,1) =
1 2
2 3
M(:,:,2) =
5 9
1 4
The first slice is the matrix [1,2; 2,3] and the second slice is [5,9; 1,4]. From what it looks like, you would like the mean of only the first column of every slice and return this as a single vector of values. Therefore, use the mean function and index into the first column for all rows and slices. This will unfortunately become a singleton 3D array so you'll need to squeeze out the singleton dimensions.
Without further ado:
O = squeeze(mean(M(:,1,:)))
We thus get:
>> O = squeeze(mean(M(:,1,:)))
O =
1.5000
3.0000
Related
For my project I need to save vectors in a matrix, thus creating a multidimensional array (3D-Matrix).
Now I'm wondering on how to access my vectors.
Lets say I have a lot of vectors stored in an array c. I could access all vectors with c(i,:).
I can also perform vector operations and use buit in fuctions like norm(c(1,:))and it gives me the absolute value of the vector. Everythings fine
Now if I store a vector v in a 2D-matrix M, i can still access every element of the vector, but M(i,j,:) doesnt give me the output [vx;vy;vz]I'm looking for. Instead matlab gives three outputs resulting in problems using the built in vector operations.
Is there any way around this?
Or do I have to implement my own functions to operate on a 3d-matrix?
Edit:
If z is a vector, the output is: z = [zx zy zz]
If this vetor is stored in a 2x2x3 matrix M(2,2,3), lets say in M(1,1), the output when accessing the vector by M(1,1,:)isnt [zx zy zz].
Instead the output is: M(:,:,1) = zx M(:,:,2) = zy M(:,:,3) = zz
Thanks for pointing out to change the direction the vector is stored in the matrix.
M(i,j,:) returns a 1×1×3 array, which Matlab understand is not exactly a vector v as you want, but a three-dimensional array, which happens to have only one element with respect to the first and second indices.
You can easily remove the dimensions of length 1 with the built-in function squeeze:
A = zeros(1,1,3);
A(:,:,1:3) = [1 2 3]
A =
A(:,:,1) =
1
A(:,:,2) =
2
A(:,:,3) =
3
B = squeeze(A)
B = 3×1
1
2
3
Say A is a 3x4x5 array. I am given a vector a, say of dimension 2 and b of dimension 2. If I do A(a,b,:) it will give 5 matrices of dimensions 2x2. I instead want the piecewise vectors (without writing a for loop).
So, I want the two vectors of A which are given by (a's first element and b's first element) and (a's second element and b's second element)
How do I do this without a for loop? If A were two dimensions I could do this using sub2ind. I don't know how to access the entire vectors.
You can use sub2ind to find the linear index to the first element of each output vector: ind = sub2ind(size(A),a,b). To get the whole vectors, you can't do A(ind,:), because the : has to be the 3rd dimension. However, what you can do is reshape A to be 2D, collapsing the first two dimensions into one. We have a linear index to the vectors we want, that will correctly index the first dimension of this reshaped A:
% input:
A = rand(3,4,5);
a = [2,3];
b = [1,2];
% expected:
B = [squeeze(A(a(1),b(1),:)).';squeeze(A(a(2),b(2),:)).']
% solution:
ind = sub2ind(size(A),a,b);
C = reshape(A,[],size(A,3));
C = C(ind,:)
assert(isequal(B,C))
You can change a and b to be 3d arrays just like A and then the sub2ind should be able to index the whole matrix. Like this:
Edit: Someone pointed out a bug. I have changed it so that a correction gets added. The problem was that ind1, which should have had the index number for each desired element of A was only indexing the first "plane" of A. The fix is that for each additional "plane" in the z direction, the total number of elements in A in the previous "planes" must be added to the index.
A=rand(3,4,5);
a=[2,3];
b=[1,2];
a=repmat(a,1,1,size(A,3));
b=repmat(b,1,1,size(A,3));
ind1=sub2ind(size(A),a,b);
correction=(size(A,1)*size(A,2))*(0:size(A,3)-1);
correction=permute(correction,[3 1 2]);
ind1=ind1+repmat(correction,1,2,1);
out=A(ind1)
I have a 4-D array in R and I want to average my array over the fourth dimension so that it gets reduced to a 3-D array. Is there a simple command to do this or is it faster to just do it inside of a for loop?
For example, imagine I have the following 4-D array A and I want some code that would produce the answer in A.mean
A = array(2,c(3,4,2,2))
A[,,,2] = 3
A.mean = array(2.5,c(3,4,2))
We can use
apply(A, c(1,2,3), FUN=mean)
I have a two arrays within a <1x2 cell>. I want to permute those arrays. Of course, I could use a loop to permute each one, but is there any way to do that task at once, without using loops?
Example:
>> whos('M')
Name Size Bytes Class Attributes
M 1x2 9624 cell
>> permute(M,p_matrix)
This does not permute the contents of the two arrays within M.
I could use something like:
>> for k=1:size(M,2), M{k} = permute(M{k},p_matrix); end
but I'd prefer not to use loops.
Thanks.
This seems to work -
num_cells = numel(M) %// Number of cells in input cell array
size_cell = size(M{1}) %// Get sizes
%// Get size of the numeric array that will hold all of the data from the
%// input cell array with the second dimension representing the index of
%// each cell from the input cell array
size_num_arr = [size_cell(1) num_cells size_cell(2:end)]
%// Dimensions array for permuting with the numeric array holding all data
perm_dim = [1 3:numel(size_cell)+1 2]
%// Store data from input M into a vertically concatenated numeric array
num_array = vertcat(M{:})
%// Reshape and permute the numeric array such that the index to be used
%// for indexing data from different cells ends up as the final dimension
num_array = permute(reshape(num_array,size_num_arr),perm_dim)
num_array = permute(num_array,[p_matrix numel(size_cell)+1])
%// Save the numeric array as a cell array with each block from
%// thus obtained numeric array from its first to the second last dimension
%// forming each cell
size_num_arr2 = size(num_array)
size_num_arr2c = num2cell(size_num_arr2(1:end-1))
M = squeeze(mat2cell(num_array,size_num_arr2c{:},ones(1,num_cells)))
Some quick tests show that mat2cell would prove to be the bottleneck, so if you don't mind indexing into the intermediate numeric array variable num_array and use it's last dimension for an equivalent indexing into M, then this approach could be useful.
Now, another approach if you would like to preserve the cell format would be with arrayfun, assuming each cell of M to be a 4D numeric array -
M = arrayfun(#(x) num_array(:,:,:,:,x),1:N,'Uniform',0)
This seems to perform much better than with mat2cell in terms of performance.
Please note that arrayfun isn't a vectorized solution as most certainly it uses loops behind-the-scenes and seems like mat2cell is using for loops inside its source code, so please do keep all these issues in mind.
i am looking for a way that i can add up elements in an array such that the first element of the first array is added to every element in the second array, then the second element in the first array is added to all every element in the second array and so on. The final vector will be length(a)*length(b) long
for example...
a=[1,2,3,4] b=[5,6,7]
answer =
[(1+5),(1+6),(1+7),(2+5),(2+6),(2+7),(3+5),(3+6),(3+7),(4+5),(4+6),(4+7)]
=[6,7,8,7,8,9,8,9,10,9,10,11]
Read up on bsxfun. It's very useful for this kind of things (and usually faster than arrayfun or for loops):
result = bsxfun(#plus, a(:).', b(:)); %'// matrix of size numel(b) x numel(a)
result = result(:).'; %'// linearize to a vector
Or, a little more freak: kron does what you want with products instead of sums. So:
result = log(kron(exp(a),exp(b)));
My first thought is to do this with arrayfun using an anonymous function that adds each scalar element of a to the full array in b. Then since you get a cell array result you can expand that cell array into the array you are looking for:
>> a=[1,2,3,4], b=[5,6,7]
>> result = arrayfun(#(x) x+b, a,'UniformOutput',false);
>> result = [result{:}]
result =
6 7 8 7 8 9 8 9 10 9 10 11
Use meshgrid to create matrices of a and b and use matrix addition to compute a+b
a=[1,2,3,4], b=[5,6,7]
[A_matrix,B_matrix] = meshgrid(a,b)
result = A_matrix + B_matrix
result = result(:)'